He now faces a more daunting test as the general election campaign begins. Alison Lundergan Grimes, who handily won the nomination in the state’s Democratic primary, is running even with the five-term Senate veteran in the polls as she seeks to unseat a major leader of Congress.

Tuesday was a rough day for the tea party movement. Not only was Bevin crushed, but Karen Handel, the Tea Party Express choice in Georgia’s Republican Senate primary, ran third and failed to qualify for the July 22 runoff election.

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Businessman David Perdue, stressing his private-sector experience as he bashed all things Washington, led five rivals and will face runnerup Rep. Jack Kingston in the runoff.

After Handel in third place, two other staunch conservatives, Reps. Paul Broun and Phil Gingrey, were far behind.

Perdue’s Republican opponents tried vigorously to stagger him, questioning his business record and accusing him of trying to buy the race. But in a year when voters are angry at Washington, his message had been resonating.

The runoff winner will face Democrat Michelle Nunn, daughter of popular former Sen. Sam Nunn, who easily won her party’s primary Tuesday. She leads most of the potential general-election rivals, though Perdue leads in some surveys.

Democrats took the spotlight in Pennsylvania, where voters soundly rejected a longtime congresswoman’s bid for the gubernatorial nomination to challenge Republican incumbent Tom Corbett. Businessman Tom Wolf crushed Rep. Allyson Schwartz after he flooded the state with ads stressing his independence from Washington.

Also in a Democratic primary, former Rep. Marjorie Margolies, the mother-in-law of Chelsea Clinton, was trounced in her bid for a comeback. Margolies served one term in the early 1990s, and the Clintons had boosted her campaign this time.

Also voting Tuesday were Arkansas and Oregon. In Arkansas, Sen. Mark Pryor, a Democrat, faces a tough fight to hold his seat against Republican Rep. Tom Cotton. Both were unopposed Tuesday in party primaries. In Oregon, physician Monica Wehby won the Republican nomination, and will face Democratic Sen. Jeff Merkley, who easily won his primary.

McConnell’s task now is to woo independent voters he’d largely shunned as he fought the thunder from the right.

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McConnell, though, has deep Republican roots. He has a strong network of backers, built from his years as the architect of the modern Kentucky Republican Party, the winner of five statewide elections and a veteran of all kinds of state political wars.

He knew how to adapt. He made sure that ads and surrogates defined the barely known Bevin in unflattering terms. He hired a top Paul adviser to manage his campaign. He began highlighting his fealty to staunch conservative causes. In March, he appeared before the much-watched Conservative Political Action Conference holding a rifle over his head; it was a gift to Sen. Tom Coburn, R-Okla., a conservative hero for his relentless commitment to their agenda.

Tea party loyalists remained wary. The Tea Party Patriots Citizens Fund, the Senate Conservatives Fund and other like-minded groups pumped money and resources into defeating McConnell.

They viewed McConnell, Senate Republican leader since 2007, as too willing to compromise and cited votes such as his backing of the 2008 Troubled Asset Relief Program, which helped ailing financial institutions, as evidence.

McConnell now has to keep the conservatives with him _ and hope they turn out in November _ while reminding Kentucky voters that he’s the same can-do lawmaker they’ve elected repeatedly since 1984. He’s also pushing hard the idea that he could become the Senate’s most powerful figure, while a Grimes vote is a vote for keeping Majority Leader Harry Reid, a Nevada Democrat, in power.

Republicans need a net gain of six seats to take control of the Senate, and analysts rate that a decent possibility. Seven Democratic-held seats are in states where Republican Mitt Romney beat President Barack Obama in 2012, while Obama states Colorado, Michigan and New Hampshire are in play.

Democrats’ best hopes for upending Republicans are in Kentucky and Georgia, and wins by candidates acceptable to mainstream Republicans _ and perhaps independents _ make that task more difficult.

In Idaho, the winner of Tuesday’s primary is likely to have little trouble winning the seat. Simpson won in 2012 with 65 percent of the vote. He has a reputation as a consensus-seeker; in 2008, Esquire magazine named him one of Congress’ 10 best members, praising his ability to find “common ground.”